## Fresnel Lenses

abishur
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### Fresnel Lenses

I clearly think a lot of the people who post in this forum, I've asked this in a projector forum and got zero responses (it's the busiest forum I could find on projectors and its completely dead), so hopefully I can get a good answer from y'all or a good resource to ask this in instead

I'm having some fun making a projector. I've learned a lot about the how and why of projectors but one of the last hurdles for me is the Fresnel lens. For instance I've figured out that if I get a Fresnel lens with a 220mm Focus length, then I would put that 220mm from my light source, but how am I choosing that distance?

My assumption is I take my light source, a 100W LED, and find it's viewing angle (which should be 60 degrees if I put a reflector behind it), and then find the distance where there light hits the top and bottom of the screen perfectly.

So I'd cut the screen in half to get the following nice right triangle

Code: Select all

``````light
*
| \
|   \
x  |     \ h
|      \
|_ _ _ _\
y``````
where * is the angle of the triangle at the light source, h is my hypotenuses, x is the distance to the screen I'm trying to find, and y is the height of the screen.

I know that y is half my screen height (4.5") and * is the viewing angle of the LED divided in half (30 degrees).

So h would be y/sin(*) or h = 4.5/sin(30) or h = 9

and x would be h times cos(*) or x = 9 times cos 30 or x = 7.79422863406 inch (~197mm)

So, if this is all correct, then I'd want a Fresnel lens with a focus length of 200mm, right?
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drgeoff
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### Re: Fresnel Lenses

What is the function of the lens?

Basic lens equation 1/u +1/v = 1/f

where u is distance between object and lens, v is distance between lens and image and f is focal length.

Magnification (image size to object size) is v/u.
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abishur
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### Re: Fresnel Lenses

The Fresnel lens takes light being shone behind it at various angles and straightens them out so they are parallel to each other and hit the screen at a 90 degree angle to maximize its efficiency.
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W. H. Heydt
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### Re: Fresnel Lenses

For optical calculations, treat the Fresnel lens as a planoconvex (flat on one side, convex on the other) of the specified focal length. That it is "Fresnel" is just a way of making the lens lighter and thinner than it otherwise would be.

abishur
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### Re: Fresnel Lenses

W. H. Heydt wrote:For optical calculations, treat the Fresnel lens as a planoconvex (flat on one side, convex on the other) of the specified focal length.
Would it surprise you to know I have no idea how to practically apply that sentence?
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drgeoff
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### Re: Fresnel Lenses

abishur wrote:The Fresnel lens takes light being shone behind it at various angles and straightens them out so they are parallel to each other and hit the screen at a 90 degree angle to maximize its efficiency.
That's fine if you are making a torch. You place the light source behind the lens at a distance equal to the focal length. The size of the screen and the distance away don't come into it. The diameter of the bright area on the screen will be the smaller of the
lens diameter or twice the light to lens distance times the tangent of half the light's viewing angle.

But I presume you want some sort of image on the screen. What is producing the image you want projected and where is it in relation to the lens?

A Fresnel lens works just the same as a non-Fresnel lens. It bends rays of light passing through it. Same formulae apply.
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Lob0426
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### Re: Fresnel Lenses

I found lens from 2x3 to 8x11 on EBAY. Some were really large, like 51" Most are 3x or 6x. Very few describe the focal length. I saw a 5x7 that might be close.

http://www.ebay.com/bhp/fresnel-lens

http://www.ebay.com/itm/FRESNEL-LENS-DI ... 1553288259
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toxibunny
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### Re: Fresnel Lenses

drgeoff wrote:
abishur wrote:The Fresnel lens takes light being shone behind it at various angles and straightens them out so they are parallel to each other and hit the screen at a 90 degree angle to maximize its efficiency.
That's fine if you are making a torch. You place the light source behind the lens at a distance equal to the focal length. The size of the screen and the distance away don't come into it. The diameter of the bright area on the screen will be the smaller of the
lens diameter or twice the light to lens distance times the tangent of half the light's viewing angle.

But I presume you want some sort of image on the screen. What is producing the image you want projected and where is it in relation to the lens?

A Fresnel lens works just the same as a non-Fresnel lens. It bends rays of light passing through it. Same formulae apply.
the image producing lens is on the other side. OP is asking about a 'collimating' lens placed between the lcd and bulb...

The lumenlabs forums used to be the best place to ask, but since cheap projectors became available, they lost a lot of relevance...
note: I may or may not know what I'm talking about...

Ravenous
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### Re: Fresnel Lenses

abishur wrote:So, if this is all correct, then I'd want a Fresnel lens with a focus length of 200mm, right?
I think that's correct. (My optics is very rusty, if lenses can get rusty!)

I forgot all the lens equations, but I think 200mm length means a magnifying glass of around 2x-3x. So if you can find a fresnel lens saying around "3x" I guess it will be in the right ballpark... a higher magnification would mean a smaller area covered.

(I've never noticed these "lenses" being sold with a focal length, only 2x/3x/4x for example.)

drgeoff
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### Re: Fresnel Lenses

toxibunny wrote:
the image producing lens is on the other side. OP is asking about a 'collimating' lens placed between the lcd and bulb...
The questions I have asked abishur were seeking to establish if that is his requirement. If it is then his discussion mentioning screen size is confusing when the word "screen" in the context of "projector" usually means the large white area that the viewed image falls on.

Yes the clue was "4.5 inch".
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Ravenous
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### Re: Fresnel Lenses

Good point about the screen, etc.

To clarify, my comment above was about the condenser (to concentrate the light source) and not the actual projector (which would require a proper projection lens, or at least something adapted from something else.) I was talking about something like an overhead projector, which uses a fresnel lens just before the slide/transparency, and a proper glass lens after it to focus on the screen.

I built my own very simple enlarger years ago for B&W printing, but note it used a simple diffusion light source, not a condenser arrangement which I think we're talking about here.

drgeoff
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### Re: Fresnel Lenses

A collimating lens will need to be no smaller than the LCD panel and it is the diagonal of the panel (not the height) which should be used in the calculation.
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abishur
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### Re: Fresnel Lenses

Man, I knew you guys would have the answers!

Let me see if I can answer all the questions
drgeoff wrote:But I presume you want some sort of image on the screen. What is producing the image you want projected and where is it in relation to the lens?
and
drgeoff wrote:If it is then his discussion mentioning screen size is confusing when the word "screen" in the context of "projector" usually means the large white area that the viewed image falls on.

I'm making a diy projector, I've chosen a 10.1" 1920x1200 LCD "screen" (which I will just refer to as the LCD panel from now on to avoid confusion with the actual screen that I will be projecting the image onto). The specs claim the viewing area is 9x6", so half my vertical viewing angle is where I got the 4.5" number from.

My light source is a 100w cool white LED. I know that I should have my LED an equal distance from the collimator's Focal length, but I have not been able to get a firm grasp on how I'm supposed to choose that focal length. Do I want to place it such that the LED's view angles perfectly hit the top and bottom of my Fresnel lens? Or should I just blindly follow all the guides I've seen out there and use a 220mm Focal length for the collimator?

So my build will be Light source (100w LED with a reflector) -> a distance equal to my collimator focal length (which is what I'm trying to learn how to calculate) -> collimator -> LCD panel -> condensor w/ 330mm focal length -> Triplet lens

I've thought about putting a piece of glass between the LED and the collimator as I've seen recommended with using other light sources to protect everything else from the heat of the light, but the LED shouldn't put out that much heat (well it shouldn't radiate that much heat, it will need a heatsink of its own)
toxibunny wrote:The lumenlabs forums used to be the best place to ask, but since cheap projectors became available, they lost a lot of relevance...
They are completely gone, in fact, much to my horror. I tried asking about this over at diyaudio in their projectors subforum, but no one is talking. I mean not even a derisive "can't you google this?" response, just pure crickets!
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Ravenous
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### Re: Fresnel Lenses

In that case I think your arrangement is right, except I don't think you need a second condenser:
LED -> a distance equal to fresnel lens focal length -> fresnel lens -> LCD panel -> Triplet lens
Problem 1 - I'm not sure a reflector behind the LED is needed, if it's radiating everything forwards

Problem 2 - LED might not illuminate evenly in practice - anyone got any ideas?

Problem 3 - just an idea - if you have a shorter focal length on the Fresnel lens (or move the LED back a bit), the illumination going through the LCD panel won't be parallel any more, but will start to converge inwards to the main imaging lens. This may increase your illumination. I found a ray diagram for an overhead projector earlier that showed this, but I lost the link

By the way, you might like to have a quick play with this program: (I don't remember if it can do point light sources, or just parallel)
http://arachnoid.com/OpticalRayTracer

EDIT: don't forget Dr Geoff's comment above, about using the diagonal of your panel, not the width, in calculations. Because the LED's output is a circle/cone. Around 10-11 inches, not 9 inches.

abishur
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### Re: Fresnel Lenses

Ravenous wrote:In that case I think your arrangement is right, except I don't think you need a second condenser:
I've seen some designs where they use the one fresnel lens, but there is some benefit to using the split fresnel design where one acts as a collimator and the other as a condensor, so I opted for that design even though it add another 20-30 dollars to the project.
Problem 1 - I'm not sure a reflector behind the LED is needed, if it's radiating everything forwards
Me neither to be honest I had thrown that in the decrease the viewing angle of the LED and make sure that less of the light was lost hitting the walls and more of it hit the collimator.
Problem 2 - LED might not illuminate evenly in practice - anyone got any ideas?
I thought that this was more or less the point of the collimator Fresnel lens? To take light that was hitting at uneven and random angles and (within reason) create an even distribution of "parallel" light lines.
Problem 3 - just an idea - if you have a shorter focal length on the Fresnel lens (or move the LED back a bit), the illumination going through the LCD panel won't be parallel any more, but will start to converge inwards to the main imaging lens. This may increase your illumination. I found a ray diagram for an overhead projector earlier that showed this, but I lost the link
I think that is one of the main benefits to the un-split Fresnel designs.
EDIT: don't forget Dr Geoff's comment above, about using the diagonal of your panel, not the width, in calculations. Because the LED's output is a circle/cone. Around 10-11 inches, not 9 inches.
Hmm... I suppose I hadn't thought about that since I was using one of those square 100w LEDs.
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Ravenous
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### Re: Fresnel Lenses

Some other diagrams before I forget:
http://hkier.fed.cuhk.edu.hk/journal/wp ... _85-95.pdf
Indeed the collimator/condenser arrangement near the olde fashioned bulb is a bit more complicated than I thought...

toxibunny
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### Re: Fresnel Lenses

the collimator lens doesn't collect/straighten out random rays - rather it straightens out rays radiating out from a *point*. since those high-power leds aren't point light sources, anything you do will be a bit of hope and fudge. best to construct your box 'close enough', and with adjusting screws for the led placement, and then do it by eye, I reckon.
The 'random rays' bouncing around behind the lcd are just noise, and should be gotten rid of by coating the inside of your box with black felt/cloth/something like that.

Source: I used to read lumenlabs forums a lot. my 'projector' was a stripped lcd screen on top of an overhead projector, cardboard and blu-tack...
note: I may or may not know what I'm talking about...

abishur
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### Re: Fresnel Lenses

toxibunny wrote:the collimator lens doesn't collect/straighten out random rays - rather it straightens out rays radiating out from a *point*.
hmm... I think I see the difference you're making the LED is more of a light area, but the fresnel lens is designed to work of a single point. I could use a more traditional light source I suppose or I could move the collimator so the focus point was just behind the LED such that the top and bottom of the LED arrary were connecting with the lines stretching on the focal point? (if that makes sense)
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toxibunny
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### Re: Fresnel Lenses

I don't think it really works like that, unfortunately. All real-world designs involve compromises of one sort or another - going with an led and a fresnel is prioritising power-efficiency, cool running, lightweightness, relative cheapness and availability. you could build a more 'perfect' projector with large heavy glass lenses and proper projector bulbs or even an arc lamp, but then you're talking hundreds if not thousands of dollars in components and a big problem with heat.

I'd certainly go the led route myself, nowadays. I guess I'd consider a car headlight bulb, but would definitely go led first. I've actually got a couple of OHP bulbsin a box somewhere, but the power/voltage requirements were weird, and I could never find anything to power them properly...
note: I may or may not know what I'm talking about...

abishur
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### Re: Fresnel Lenses

Let me ask one more question, I've been doing more research into my lighting options and keep coming back to this very nice sweat spot of performance (advertised lumens) vs price of the 100w LED array. I thought about jumping up to 150w or 200w, but the price makes a major jump, so maybe if the projector does a good enough job I can do an "lamp" upgrade one day.

Regardless I want to minimize my loss of light. Apparently reflectors are somewhat pointless with LEDs (who knew?), but what if I put a convex lens over the array to focus it? It might be difficult to match the focal length of the condenser lens to the focal length of the collimator Fresnel lens, but what do you think?
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Ravenous
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### Re: Fresnel Lenses

If the LED doesn't cover the back of the large fresnel lens & the panel neatly, I suppose you could use a lens near the LED to widen or narrow the beam to get more coverage. I think this is what the condenser lenses are needed for in regular projectors (probably hefty heatproof things...)

(I've never had a proper projector apart... they were always far too expensive for me to get one!)

rotwang
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### Re: Fresnel Lenses

If you take a look at a100W LED you'll see that it consists of an array of smaller leds, in my case a 10x10 array of 1watt leds, and is physically about 20mm x 20mm. This in no way resembles a point light source, which all the discussions about fresnels seem to assume. The best you're going to get is a 10x10 array of bright spots. And by the way the beam angle from those arrays is something like 140 to 150 degrees. There are very specialised optics which will capture that light and homogenise it, but you don't want to know about the prices.
Regardless of what anyone else tells you, these arrays need to be mounted to a fan cooled heatsink with proper thermal compound (I can recommend old pentium heatsinks which are generally rated up to 150watts) and MUST ONLY be driven from constant current power supplies, you can't get away with a series resistor (well not for very long). I've been trying to find a cheap way of using the led arrays, and the best I've managed so far is a fairly uniform patch of light about 20mm square, at the expense of loosing more than half of the original light from the array.

One other note of warning, some constant current supplies take a second or more to turn on their output after you turn on the mains. Three guesses how long it takes to lean round the front of the LED to see why nothing seems to be happening? 10000 lumens won't blind you, as long as it isn't focussed by a lens, but it sure takes awhile for the big green after image to fade away.
Roger
abishur wrote:Let me ask one more question, I've been doing more research into my lighting options and keep coming back to this very nice sweat spot of performance (advertised lumens) vs price of the 100w LED array. I thought about jumping up to 150w or 200w, but the price makes a major jump, so maybe if the projector does a good enough job I can do an "lamp" upgrade one day.

Regardless I want to minimize my loss of light. Apparently reflectors are somewhat pointless with LEDs (who knew?), but what if I put a convex lens over the array to focus it? It might be difficult to match the focal length of the condenser lens to the focal length of the collimator Fresnel lens, but what do you think?

Ravenous
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### Re: Fresnel Lenses

rotwang wrote:physically about 20mm x 20mm. This in no way resembles a point light source, which all the discussions about fresnels seem to assume.
Phew, good information! I hadn't realised they needed to be that big...

By the way my assumption in everything above was: as long at the light is fairly well spread when it reaches the fresnel plate things would be OK - because the fresnel just redirects the illumination towards the imaging lens, not actually images. If this is wrong then a rethink's required...

abishur
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### Re: Fresnel Lenses

rotwang wrote: And by the way the beam angle from those arrays is something like 140 to 150 degrees. There are very specialised optics which will capture that light and homogenise it, but you don't want to know about the prices.
The beam angle was one of the reason I was thinking about a reflector (which was supposed to limit the angle to 60 degrees) and why I was also inquiring about the use of a convex lens to take those disjoint light sources and condense down to a smaller point. I'd be very much interested in knowing the prices / what are they called / how one would Google for them.
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